The 3D Spin Geometry of the Quantum Two-Sphere
Quantum Algebra
2015-05-18 v2 Mathematical Physics
math.MP
Abstract
We study a three-dimensional differential calculus on the standard Podles quantum two-sphere S^2_q, coming from the Woronowicz 4D+ differential calculus on the quantum group SU_q(2). We use a frame bundle approach to give an explicit description of the space of forms on S^2_q and its associated spin geometry in terms of a natural spectral triple over S^2_q. We equip this spectral triple with a real structure for which the commutant property and the first order condition are satisfied up to infinitesimals of arbitrary order.
Cite
@article{arxiv.1003.2150,
title = {The 3D Spin Geometry of the Quantum Two-Sphere},
author = {Simon Brain and Giovanni Landi},
journal= {arXiv preprint arXiv:1003.2150},
year = {2015}
}
Comments
v2: 25 pages; minor changes